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And here I’m talking about the search pages powered by APIs not those one which forward you to the google web site
is that will affect the PR or not
examples of sites powered by google with API
www.cnn.com
google.btopenworld.com/dynamic/search/google_search_panel.jsp
[web.icq.com...]
But if they didn't exclude it, is that means that cnn linking to your web site
Yes, but unless CNN link to this specific SERP themselves (highly unlikely) then its not going to pass on any of CNN's page rank.
What will in fact happen (disclaimer: based on my understanding of PR) is that your link will provide this page with all its PR. This will get passed to all the pages this SERP links to - probably some internal links to CNN + the sites linked in the search results themsleves.
So you will get a small fraction of the PR you gave it in the first place, as will the other sites listed in the SERP - probably your competitors.
It seems quite a few people are doing this at the moment - a number of my backlinks listed by Google are SERP pages. Which is nice for me, but I don't think it is what was intended.